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InterviewSolution
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Write about the postulates of Boolean Algebra. |
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Answer» Postulates of Boolean Algebra: Boolean Algebra is an algebraic structure defined on a set of elements B together with two binary operators + and . provided the following postulates are satisfied: (1) (a) Closure with respect to the operator + (b) Closure with respect to the operator. (2) (a) An identity element with respect to +, designated by 0 : X + 0 = 0 + X = X. (b) An identify element with respect to designated by 1 : X . 1 = 1 . X = X. (3) (a) Commutative with respect to + : X + Y = Y + X (b) Commutative with respect to . : X . Y = Y . X (4) (a) . is distributive over : : X . (Y + Z) = (X . Y) + (X . Z) (b) + is distributive over . : X + (Y . Z) = (X + Y) . (X + Z) (5) For every element X ∈ B, there exists an element \(\bar { X }\) ∈ B such that: (a) X × \(\bar { X }\)= 1 (b) X . \(\bar { X } \) = 0 The postulates listed above are called Huntington (1904) Postulates and need no proof. They are used to prove the theorems of Boolean Algebra. |
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